A piece of paper TUVW has the precise shape of a square, with each side length being 20 units. The point M is the midpoint of side TU and N is the midpoint of TW.
The paper is now folded along the line MN such that the point T touches the paper. The point V is then folded over a line PQ parallel to MN such that V lies on MN.
Determine the area of the hexagon NMUPQW.